With this case the fan should connected directly with the RPi5 pcb. If there is a fan control working or not, massively depends on your chosen distribution. The argonneo5.sh installs no daemon for that, to provide an interface is the task of a recent kernel. Some distributions let you set the thresholds via dtparam, others need an additional daemon for that…
To temporary shutdown the fan, you can try this command: echo "0" | sudo tee /sys/class/thermal/cooling_device0/cur_state